For improved color stability and reproducibility, the recent image forming apparatuses such as copiers or printers may be managed using spectrometers such as spectrophotometers, as described in Japanese Patent Application Publication No. 2007-208708. For example, the spectrometer measures the diffused lights reflected from the output image to obtain the spectral reflectance. Based on the spectral reflectance, various parameters in the color system, such as XYZ or L*a*b* color system, are obtained. The obtained parameters may be used to evaluate color tone of the image or to correct image forming conditions of the image forming apparatus. However, in case the image forming apparatus outputs images at high speeds, inline measurement using the spectrometer has been difficult as detection speeds at the spectrometer are slower than the printing speeds.
In view of the above, the spectral reflectance of a target object, such as the output image, is usually estimated by obtaining a transformation matrix that converts the light intensity signal detected at the spectrometer to the spectral reflectance, based on measurement results of a plurality of color samples whose spectral reflectance are known, for example, as described in Tsumura, et al., Estimation of Spectral Reflectances from Multi-Band Images by Multiple Regression Analysis, Optical Society of Japan, KOGAKU, Japanese Journal of Optics, Vol. 27, No. 7, 1998, pp. 384-391.
Tsumura, et al. estimates spectral reflectance from multi-band images using the multi-regression analysis. In the analysis, the pixel values of the multi-band images and the higher order terms of the pixel values are used as explanatory variable, and the spectral reflectance is used as objective variable, thus improving estimation accuracy. For example, assuming that the second order term is used, the spectral reflectance r is calculated based on the light intensity signals s1 to sm measured for m wavelength bands, using the extended sensor response vector v′=[s1, s2, . . . , sm, s1*s1, s2*s2, . . . , sm*sm].